Cellular automata as the basis of integrated dynamic regional modelling

Transcription

1 Environment and Planning B: Planning and Design 1997, volume 24, pages Cellular automata as the basis of integrated dynamic regional modelling R White Department of Geography, Memorial University of Newfoundland, St John's, Newfoundland, Canada; roger@morgan.ucs.mun.ca G Engelen Research Institute for Knowledge Systems, Postbus 463, 6200 AL Maastricht, The Netherlands; guy@riks.nl Received 9 October 1995; in revised form 7 March 1996 Abstract. We present an integrated model of regional spatial dynamics consisting of a cellular automaton-based model of land use linked both to a geographic information system (GIS) and to standard nonspatial models of regional economics and demographics, as well as to a simple model of environmental change. The operation of the model is illustrated with an application to the island of St Lucia developed for the purpose of providing insights into the possible socioeconomic consequences for the island of global climate change. On the basis of resultsfromthis and other applications of the model, we conclude that cellular automata not only permit a detailed modelling and realistic prediction of land-use patterns, but they also provide a means of introducing the effects of spatially localized environmental factors, as represented in the GIS, into the operation of standard economic and demographic models, which are otherwise unconstrained. 1 Introduction Cellular automata (CA) are rapidly gaining favour among geographers as a tool for modelling spatial dynamics (Batty and Xie, 1994; Cecchini and Viola, 1992; Couclelis, 1985; 1989; Engelen et al, 1993; 1996; Phipps, 1989; White and Engelen, 1993; 1994b; White et al, 1997). In comparison with traditional approaches based on differential or difference equations, the advantages are obvious: CA are inherently spatial, with rulebased dynamics, and the consequent computational efficiency means that dynamics can be modelled with a very high spatial resolution. Retention of spatial detail is important for several reasons, not least because the system dynamics may depend in crucial ways on spatial details (White and Engelen, 1994a). The desirability of a link to geographic information systems (GIS) is also clear, as GIS are typically the repository of the high-resolution data to which the CA could be applied, although the majority of cellular models to date have not been linked to a GIS. Linking cellular automata to GIS would overcome some of the limitations of current GIS. Couclelis (1991) has pointed out that, although GIS have been quite useful in planning applications in such areas as resource management and rural planning their appearance on the urban and regional planning scene has been much more "hesitant" (page 10), essentially because a GIS always provides "... information about spatial objects... contained in space. Missing almost entirely are nonlocalized spatial notions such as spatial organization, configuration, pattern, spatial process, spatial dynamics, restructuring, transformation, change. Yet these are all notions that are central in urban and regional studies, and they underlie urban and regional planning especially at the strategic level" (page 15). Cellular automata, precisely because they represent these spatial processes, show great promise as a basis for urban and regional modelling; and in this role they may provide a link between the spatial data sets of GIS and the highly aggregated models of regional science and economics. In this paper we demonstrate the integrative role of a

2 236 R White, G Engelen cellular automaton-based regional model. Furthermore, the papers in this issue by Phipps and Langlois (1997), and by Batty and Xie (1997) also address this point. In the following section we present an integrated model of regional dynamics consisting of a cellular automaton linked both to a GIS and to standard models of regional economics and demographics, as well as to a simple model of environmental change. The operation of the model is then illustrated with an application to the island of St Lucia developed for the purpose of providing insights into the possible socioeconomic consequences for the island of global climate change. On the basis of results from this and other tests of the model, implications for the use of integrated dynamic spatial models are discussed. 2 An integrated cellular automata-based model of regional dynamics Standard CA (for example, see Gutowitz, 1991) have implicitly been formulated to maximize their generality. They thus have two characteristics which are of concern in the context of urban and regional modelling. (1) They are defined on a homogeneous cell space. In other words, a cell is completely characterized by its state value, which may of course change from time to time in accordance with the transition rules. Cells have no inherent qualities that can affect the transitions, so a given configuration of cells in the neighbourhood of a cell will result in the same state transition regardless of the location of the cell on the grid. (2) They are unconstrained, so that the total number of cells in each state is determined endogenously by the application of the transition rules to the current configuration of cell states. But neither of these characteristics is desirable in CA designed to model land-use dynamics. Land use typically depends on three types of factors: the inherent qualities of the land itself; the effects of neighbouring land-use activities; and the aggregate level of demand for land for each activity. Traditional CA deal only with the neighbourhood effects. The inherent qualities of the land would represent inhomogeneities in the cell space, with some cells being intrinsically more desirable for certain activities than others; and the aggregate demand for land for each activity would represent an exogenous constraint on the number of cells in each state. Yet clearly a cellular automaton designed for regional modelling should encompass all three kinds of factors. Land does have qualities that make some parcels inherently more desirable for particular uses for example, slope, drainage, or legal restrictions. Neighbourhood effects of attraction and repulsion are well documented (for example, see Adams, 1994). And within a region the total amount of land used for each activity is largely determined not by local factors but by the requirements of the regional or national economy. The model presented here, in contrast with standard CA, is a constrained stochastic cellular automaton defined on a nonhomogeneous grid space. It thus deals explicitly with all three types of factors affecting land use. The model consists of three linked components (figure 1): (1) a GIS which stores relevant spatial data on land use and suitabilities for various land uses; (2) the cellular automaton itself, which represents the local spatial dynamics inherent in the system, with cell states representing land use or land cover; and (3) a macro-scale model representing the nonlocal dynamics of the population, the economy, and relevant aspects of the natural environment. (1) (1) For another example of the use of a macro-scale model in conjunction with a cellular automaton, but in which the macro model acts to introduce an inhomogeneity of the cell space, see Phipps and Langlois, 1997.

3 Cellular automata as the basis of regional modelling 237 Integrated dynamic model Micro-scale spatial cellular model GIS: geographical database Figure 1. A model consisting of three linked components. 2.1 The GIS A GIS is the logical foundation for the cellular model because it is the repository for the high-resolution spatial data which is used in the cellular automaton. In fact, a cellular automaton can be thought of as a GIS with a dynamic defined on it. With cell states representing land use, the initial state of the cellular automaton can be established in the GIS by manipulating the coverages to produce one showing land use by the categories required and at the resolution corresponding to the scale of the cellular grid. Furthermore, the state of each cell in the cellular automaton will depend in part on the inherent suitability of that cell for each possible state. As suitabilities are typically established as weighted sums of such factors as soil type, slope, precipitation, and legal restrictions on use, they are best calculated in the GIS and resampled to the

4 238 R White, G Engelen resolution of the cellular automaton. In the current model the GIS operations are performed in IDRISI (Graduate School of Geography, Worcester, MA) and exported to the cellular model as byte binary files, but a fully interactive link is possible. 2.2 The cellular automaton The cellular automaton itself is defined as follows. Each land use is represented by a cell state but these states are subdivided into two categories: functions and features. Functions are those land uses which are active, such as housing, forestry, or commerce; in principle, a cell in any one of these states can be converted to any other, though some transitions may be more likely than others. Features are those land uses which are fixed, or at least are not transformed by the normal cellular dynamics, such as water, parks, or major facilities such as airports. However, cells may occasionally be converted to or from a feature state either by a special process or by an exogenous intervention. Although feature states are not subject to state changes generated by the transition rules of the cellular automaton, they do appear as arguments in those rules and may thereby affect the state transitions of nearby function cells. Thus, for example, a cell may be fixed in a feature state representing park land but the presence of the park cell may increase the likelihood that cells in its neighbourhood will be converted to residential use. Whereas traditional CA typically use either the von Neumann neighbourhood, consisting of the four cells adjoining the sides of the given cell, or the Moore neighbourhood, composed of the eight adjacent cells, in this model the neighbourhood of a cell is defined to be all cells within a radius of six cells of the given cell, and includes the cell itself. The neighbourhood consequently consists of 113 cells. Thus in the application to St Lucia discussed below, where the cell size is 250 m, the radius of the neighbourhood is 1.5 km. As the cellular automaton is defined on a regular grid, there are 18 discrete distances within the neighbourhood; all 113 cells are situated at one of these 18 distances. For each active (that is, function) cell, a vector of potentials is calculated, with each potential representing the degree of desirability of the cell for a particular function state. The potential depends on three factors: (1) the intrinsic suitability of the cell itself, as calculated in the GIS, for the state for which the potential is being calculated; (2) the aggregate effect of the cells in the neighbourhood; and (3) a stochastic perturbation. For each cell, the potential for transition to each active state (z) is calculated as follows: p z = S Z N 2 + e z9 for all z, (1) N z = /*w z,,,,, (2) d,i where P z is the potential for transition to state z; & is the suitability of the cell for activity z, 0 ^ S z < 1; if N z < 0, S z is replaced ' by (1 - S z ); N z is the neighbourhood effect; w zyd is the weighting parameter applied to cells in state y in distance zone d\ i is the index of cells in distance zone d; e z is a stochastic disturbance term (Gaussian in the St Lucia application below); f 1, if cell / in distance zone d is in state y, I 0, otherwise.

5 Cellular automata as the basis of regional modelling 239 The heart of equation (1) is the calculation of the neighbourhood effect in equation (2), in which each cell in the neighbourhood makes a contribution depending on its state and location. It will frequently be the case that the closer a cell is, the stronger will be its effect, whether positive or negative; but it is quite conceivable that, in the case of some land uses, the effect may change sign as the distance increases. For example, retail activity may have a negative effect on the potential of a cell for residential use if the retail cell is immediately adjacent to the cell in question but may have a positive effect if it is further away. A strong positive weight on the cell itself (d = 0) for its current state provides an inertia effect and tends to keep a cell in its current state. The inertia effect would represent the consequence of the various costs incurred in changing from one land use to another. Figure 2 illustrates graphically the weighting parameters used to calculate the potential of a cell for commercial activity, as calibrated in an urban land-use application. Each line represents the weights applied to cells in the neighbourhood which are occupied by a particular land use, with the weights plotted as a function of distance. " Commerce -» Industry - «Housing - - Railway -H- Roads "~i Distance Figure 2. The weighting functions applied to calculate the potential of a cell for commercial activity. The aggregate effect of the cells in the neighbourhood is weighted by the suitability of the cell itself for the activity for which the potential is being calculated and it is then subjected to a stochastic perturbation in order to arrive at the final value of the potential [equation (1)]. The potentials of the cell for all active states (z) are calculated and it is this set of values that is used as an argument of the transition rule. The transition rule is simply that each active cell is converted to the state for which its potential is greatest but only until the demand for cells in a given state is satisfied. After that point is reached, no more cells are converted to that state; potentials for that state are ignored in determining subsequent conversions. Thus before any cells are converted all cells must be ranked by the value of their highest potential, and conversions proceed starting with the cell with the highest potential. Because of the stochastic perturbation term, ties in potential values (either between functions for a given cell or between cells) almost never occur, and so no special procedure is required to avoid the spatial bias which could otherwise be introduced through the ranking algorithm. 2.3 The macro-scale model The level of demand for cells in the various active states that is, the demand for land for various activities is provided by the macro-scale model of regional dynamics. The nature of this model varies according to the application, but in the present case it consists of three linked models.

6 240 R White, G Engelen (1) A model of the natural environment This consists only of a set of linked hypotheses about future changes in certain aspects of the environment. Specifically a hypothesis about the trend in global mean temperature is linked to hypotheses about the effect of temperature change on such factors as precipitation, storm frequency, and sea level. In turn, change in precipitation, for example is linked to a change in agricultural productivity, and change in storm frequency is assumed to affect demand for tourism. Thus this component links changes in the natural environment to changes in economic parameters. (2) A demographic model This is a very simple representation of the demographics, without disaggregation by age or sex cohorts. However, mortality and migration rates are both expressed as functions of a measure of economic well-being, so that changes in the regional population depend in part on the evolution of the economy. (3) An input-output model of the economythis provides a representation of intersectoral linkages and thus permits the effects of changes in the output of one sector on other linked sectors to be calculated. Sectors are defined so as to correspond to active landuse categories in the cellular automaton. Final demands for each sector are affected exogenously by changes in the natural environment (as in the case of a change in the demand for tourism mentioned above) and also by changes in the population generated in the demographic model; thus the economic and demographic models are joined in a relationship of mutual causation. The total intersectoral effects of the exogenous changes in final demand are calculated at each iteration by means of the Leontief inverse. The output of the macro-scale model is converted to cell-state requirements in two ways. First, the model of the natural environment generates certain cell-state changes directly, without reference to the dynamics of the cellular model. Specifically, when changing temperatures lead to a change in sea level in that model, this is translated directly into changes in the state of cells along the shore. For example, if the sea level rises, cells with sufficiently low elevations are converted from beach or mangrove to sea. In general, however, it is the demographic and economic models which generate the demand for changes in cell states, and these demands are implemented through the operation of the cellular model. Increasing population requires more cells of residential land use, and increases in the output of the various economic sectors will require additional cells in the corresponding land-use states. Changes in economic and demographic quantities are converted to cell requirements by means of productivity parameters. These parameters reflect, in a summary form, much of the information that resides at the cellular level. At initialization, productivities are calculated simply by dividing the size of each economic and demographic sector by the number of cells occupied by the corresponding land use. But in subsequent iterations the productivities must be recalculated to reflect changes both in the average suitability of the cells occupied by an activity and in the price of land. The average suitability of cells occupied by a particular land use will be altered when new cells are occupied, or existing ones lost to another land use, as in general these marginal cells will have different suitabilities than the mean suitability of all cells occupied by the activity. Productivity is assumed to depend directly on suitability. It is also assumed to depend on the price of land, with land use being intensified as prices rise. Notional prices are defined in terms of the total suitability of all cells occupied by a particular land use in relation to the total suitability of all land that could be occupied by the activity. As land for a particular activity becomes more scarce, the corresponding land price rises and, consequently, the productivity of all cells occupied by the activity increases. Thus the productivity parameters reflect the detailed environmental

7 Cellular automata as the basis of regional modelling 241 characteristics summarized in the suitability measures and the competition among the various activities for land with specific characteristics. 3 Application of the model A full integrated cellular model is obviously quite complex and therefore difficult to test comprehensively. However, the cellular model itself has been tested in an application to the city of Cincinnati, Ohio. A cellular model, with the macro-scale components replaced by a simple model representing a constant growth rate, was calibrated and then subjected to an extensive sensitivity analysis (White et al, 1997). The results indicate that this model is relatively easy to calibrate so that it generates land-use patterns similar to those of the test city. Furthermore, the calibrated patterns of weights (w zyd ) used to calculate the transition potentials are reasonable in that they reflect what is known about locational preferences in urban areas. The most difficult aspect of the calibration is to get the sets of weights corresponding to transitions to different states in reasonable balance with each other. Calibration of the stochastic perturbation term is quite straightforward, as this parameter largely determines the fractal dimension (radial dimension) of the urban land-use pattern, and this can be matched to the dimension measured for the actual city. In a subsequent investigation, the complete integrated model was run with parameter values and initial conditions typical of small Caribbean islands that is, values chosen to represent a 'generic' small island. Sensitivity analyses were performed to investigate the effect of integrating the components (Engelen et al, 1993; 1996). The results indicate that each component model tends to constrain the behaviour of the others, so that together they are less likely to give unrealistic results. The model described here is currently being calibrated for an application to the Caribbean island of St Lucia, as part of a United Nations Environment Program project on global climate change. The aim of this application is to demonstrate that the integrated cellular approach is a useful tool for exploring the possible long-term socioeconomic impacts of climate change in the Caribbean. Although the project is still underway, and a final calibration has not been arrived at, we will describe briefly one scenario based on a preliminary calibration in order to illustrate the behaviour of the model. The initial conditions for the simulation correspond to the actual state of St Lucia in The population is The birthrate is relatively high (26.9 per thousand) and only partially offset by mortality (6.3 per thousand) and net migration ( 5.8 per thousand) (Government of St Lucia, 1991b). The birth rate is assumed to decrease slowly (toward 16.7 per thousand over 40 years) and so also is the death rate (to 5.4 per thousand). The mortality and migration rates depend on the employment rate, which is used as a measure of economic well-being. GDP at market prices is US$1049 million, and the economy, represented in the input-output model by five intermediate sectors (agriculture, industry, trade, services, and tourism) and two final demand sectors (local consumption and exports), is heavily dependent on agricultural exports (primarily bananas) and tourism (Government of St Lucia, 1991a). The climate model is specified to represent a scenario in which rising temperatures lead to increasing storm frequency and precipitation, with adverse effects on the level of demand for tourism (discussions with climatologists and tourism officials indicate that this sequence of events is a likely consequence of global warming). At the cellular level, initial land use is shown in figure 3(a) (see over) (OAS, 1987). Five natural land-use categories are used: beaches, mangroves, primary forest, secondary forest, and scrub and grass. Beaches, mangroves, and primary forest are treated in the model as fixed features because change to these areas is restricted both by natural

8 242 R White, G Engelen (a) (b) Figure 3. Land use in St Lucia: (a) initial state; (b) final state (after 40 years). (A colour version is available on our website conditions and by land-use regulations. Secondary forest, and scrub and grass are active categories. There are six human occupance categories: mixed agriculture, agriculture, rural residential, urban, tourism, and airport. All are active categories except airport. Mixed agriculture consists of areas which are 20% to 70% forested, with the remaining area in agriculture; it thus represents a transitional category between agriculture and secondary forest. Agriculture, mixed agriculture, and secondary forest are among the most active categories in the model. In terms of correspondence with the macro-scale models, demand for (a) mixed agriculture and agriculture cells and for (b) tourism cells is determined by the output of the corresponding sectors in the input-output model; demand for rural residential cells is determined by the employment inputs for the agriculture sector; and the requirement for urban cells is generated by the combined outputs of the industry, trade, and service sectors of the input-output model, together with the number of nonrural residents. Suitabilities are calculated in a GIS from coverages representing slope, land-use capability for agriculture, climate regions, land-use restrictions and access to the road network (OAS, 1987) and these are then read into the cellular model. In the absence of historical land-use data that could be used for calibration purposes, the weights (w zyd ) used in equation (1) are set so that the initial land-use pattern remains essentially stable during the first few iterations. This procedure of course depends on a tacit assumption that the current land-use pattern is in equilibrium with its forcing factors, which is unlikely to be the case; but the problem may not be serious, as sensitivity analysis (White et al, 1997) has shown that the results are not highly sensitive to changes in the weights so long as the qualitative patterns of weights is approximately correct. Running the model for 40 years of this scenario gives rather gloomy results. The population grows to ; but because of the unfavourable evolution of the tourism

9 Cellular automata as the basis of regional modelling 243 sector the economy does not do as well. The employment rate falls continuously over the period, and the mortality rate, after falling for the first 30 years, begins to rise again during the last six years of the simulation. Employment in tourism grows slowly for the first 25 years and it then declines. Employment in the 'urban' sectors of industry, trade, and services increases by about 40%, but this is not enough to absorb the growing labour force. Employment in agriculture also increases, but by only about 15% because of the severe constraints imposed by the natural environment the island is steep and mountainous and has large areas that are either semiarid or too humid for agriculture. Some of the increase in agricultural production is due to expansion onto more marginal land, primarily the scrub and grass land of the coastal margin of the southern half of the island (the scrub and grass area in the northeast actually expands [(figure 3(b)]. As a result, the average suitability of land used for agriculture decrease slightly. Most of the increase in production in this sector is due to an increase in the intensity of land use, as shown by the rising land productivity parameter for agriculture. However, total output increases by substantially less than the 15%) increase in agricultural employment, resulting in an impoverishment of this sector. Changes in land use over the 40-year period are not dramatic, largely because of the strong topographic and climatic constraints [figure 3(b)]. The most visible changes are the conversion of some scrub and grass areas to agriculture mentioned above, the expansion of the rural residential zones in the valleys, and the large expansion of Vieux Fort, the urban area at the southern tip of the island. 4 Uses and misuses of the model It is not really possible to predict the state of St Lucia 40 years in the future, and so a single run of the model like that just described should not be interpreted literally. Under some circumstances, useful predictions may be possible. Experiments performed with the application of the cellular model to Cincinnati (White and Engelen, 1994b) suggest that reasonable forecasts of urban land-use patterns over a period of 10 to 15 years can be made with some confidence if the growth rate of the city is known. But that is another forecasting problem. In the case of the integrated model, the model itself may perform well (although it has not yet been tested extensively against historical data sets) but the outcome depends to a large extent on assumptions about the future behaviour of the forcing variables. In the case of St Lucia, a country with essentially no buffer between itself and events in the world economy, forecasting beyond the very short term is clearly impossible. A ruling by the European Union or the World Trade Organization which removed preferential access to the European market for St Lucia bananas would have immediate catastrophic effects. So would a decision by tourists, afraid of skin cancer, to avoid a destination known for sunny beaches. But these events, although they would not be unexpected, are essentially unpredictable. What the model can do is support 'what if experiments, allowing the user to explore various possible futures and thus to develop insights that may be of use in strategic planning. Within this context it may frequently turn out that the future is more predictable than might be expected, owing to the presence of bifurcations in the system. Bifurcations, in which new and qualitatively different solutions appear suddenly as one or more parameters pass a critical value, appear in any sufficiently nonlinear system. Whereas each of the three components of the macro level of the integrated cellular model is essentially linear, once they are linked with each other, and in particular with the cellular model, their behaviour becomes nonlinear. The most

10 244 R White, G Engelen powerful nonlinearities are due to the constraints on land use encountered at the microscale. These tend to operate as near-discontinuities, having only a marginal effect for many iterations of the model and then suddenly taking effect with full force. For example, as an activity expands it may easily occupy land of somewhat lower suitability, with only minor effects on productivity and output until suddenly no more land is accessible to that activity, and the growth of the sector is sharply curtailed, with effects that are transmitted throughout the system. Of particular interest to planners are the spatial bifurcations that may occur in the cellular model, with a dramatic change in land use appearing as a parameter value crosses a critical threshold. For example, sensitivity analysis of the 'generic' island application mentioned above included varying the birth rate. Repeated runs of the model with stochastic variations showed that the area occupied by local agriculture depended very little on the birth rate, except that in about 20% of the simulations, corresponding to the runs with the highest birth rates, a forest area on the northeast of the island was converted to agriculture (figure 4). Furthermore, the extent of this area, once it appeared, depended to only a minor degree on the actual level of the birth rate. This example suggests that it is not always necessary to have a good estimate of key parameter values in order to be able to forecast the behaviour of the system insofar as it depends on these parameters. Once the bifurcation points are identified, it is necessary only to know whether the actual value is likely to be above or below the critical value. Furthermore, as figure 4 makes clear, the state of most cells was entirely independent of the birth rate: typically, the probability of being occupied by local agriculture was either 0 or Only a relatively small number of cells, located for the most part in well-defined zones (the one in the northeast being the most prominent), were Figure 4. Map showing the probability of natural land being lost because of varying birth rate on a 'generic' island. (A colour version is available on our website

11 Cellular automata as the basis of regional modelling 245 occupied by local agriculture in some runs but not in others. The implication for land-use management is that, if, for example, it is considered desirable to protect forested land, it would be best to focus limited management resources on those forested areas which the model identifies as at risk from conversion to local agriculture. In general, use of the model to explore rather than predict the future depends on running the model repeatedly. One prediction of the future means nothing but hundreds of predictions, made under a variety of assumptions as to parameter values, permit us to extract the pattern of future possibilities. Some features will turn out to be highly robust, surviving almost any change in the assumptions as regards population growth rate, trends in demand for export products, or other factors. Other features will be highly sensitive to some of these factors but frequently, when a bifurcation effect is involved, the sensitivity will be clear-cut, even dramatic. 5 Conclusions Perhaps the most valuable aspect of CA-based modelling is that it permits socioeconomic models to be integrated in a detailed and relatively realistic way with models of the natural system, so that implications of their joint behaviour can be explored. As the CA introduce spatial dynamics essentially at the level of the GIS, which already integrates data from both realms, they are able, potentially, to capture in some detail the process of interaction between the human system and the natural environment. And it is at this very local level that most significant interactions occur, creating complex changing patterns that may seem messy if not understood as the necessary manifestation of a self-maintaining, self-organizing, evolving system. Only a very small subset of dynamical processes, those that exist at the boundary between order and chaos, to use Langton's phrase, can generate elaborate fractally dimensioned structures. But these are precisely the systems that are capable of structural evolution in a changing environment (Kauffman, 1993; Langton, 1990; Wooters and Langton, 1990). These results suggest that a safe working hypothesis would be that successful systems, whether natural or human (or natural and human), are necessarily complex and that formal techniques used to analyse or model them must be able to capture and work with that complexity. GIS, with their high level of spatial resolution, do represent the complexity we see on the land. GIS-based cellular automata retain and use the complexity to model the intricacies of local spatial dynamics. And the link with standard socioeconomic models permits a full range of interactions, from micro to macro scales, to be captured. Change is inevitable. But not all change leads to a desirable future. The present concern to find policies compatible with 'sustainability' suggests that a basic problem is to determine which changes strengthen the human-environment system and which are likely to lead to undesirable or catastrophic consequences. CA-based integrated modelling techniques should be able to help. References Adams D, 1994 Urban Planning and the Development Process (UCL Press, London) Batty M, Xie Y, 1994, "From cells to cities" Environment and Planning B: Planning and Design Batty M, Xie Y, 1997, "Possible urban automata" Environment and Planning: Planning and Design Cecchini A, Viola F, 1992, "FicTies (fictitious cities): a simulation for the creation of cities", paper presented at the International Seminar on Cellular Automata for Regional Analysis, Dipartimento di Analisi Economica e Sociale del Territorio, Universitario di Architettura di Venezia, Venice; copy available from A Cecchini, Laboratorio Didattico sulla Simulazione, Ca'Tron, S.Croce 1957, Venezia, Italy

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